In this paper, the continuous wavelet transform is studied in variable \(L^{p(\cdot )}\) spaces. Parseval relation and Reconstruction formula for the continuous wavelet transform in variable \(L^{p(\cdot )} \) spaces are derived. The characterization of variable Besov spaces associated with the continuous wavelet transform is also presented.

中文翻译：

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可变Lebesgue空间中连续小波变换的Besov范数

本文研究了在变量\（L ^ {p（\ cdot）} \）空间中的连续小波变换。推导了变量\（L ^ {p（\ cdot）} \）空间中连续小波变换的Parseval关系和重构公式。还介绍了与连续小波变换相关的可变Besov空间的特征。